Hard Eight is a term used in the game of craps, which is popular among the casino guests in Las Vegas. John has just lost all his money in Vegas when an older man who appears to be well off offers him his assistance. The man, Sydney, promises to teach John to make a living in the casinos. Later he helps John in other ways. John appears not to ask himself why Sydney is doing all that, but we, the audience, do.
Austerity and simplicity seem to have been the keywords for director-writer Paul Thomas Anderson whose first film this is. It is an impressive debut but maybe the director has been paying to much attention to style. There is not quite enough to engage us in the story.